The thermodynamical potential for dilute solutions is rederived, generalized and applied to defects in solids. It is shown that there are always defects in solids, i.e. there is no perfect solid at any finite temperature. Apart from the temperature- dependent concentration of defects, another case is presented, where the defect concentration does not depend on temperature.

M. Apostol

The stability of metallic clusters of sodium (Na) in the octahedral cages of Na-doped fullerites Na6C60 and Na11C60 is discussed within a Thomas-Fermi model. It is shown that the tetrahedral Na4-cluster in Na6C60 has an electric charge of cca. +2.7 (in electron charge units), while the body-centered cubic Na9-cluster in Na11C60 is almost electrically neutral.

M. Apostol

The excitation spectrum of the density collective oscillations is computed for multi-component molecular mixtures both with Coulomb and (repulsive) short-range interactions. Distinct sound-like excitations appear, governed by the short-range interaction, which differ from the ordinary hydrodynamic sound. The dielectric function and the structure factor are also calculated. The "two-sounds phenomenon" can be understood by means of the predictions of this model.

M. Apostol

In this paper, we introduce The 2-variable unified family of generalized Apostol-Euler, Bernoulli and Genocchi polynomials and derive some implicit summation formulae and general symmetry identities. The result extend some known summations and identities of generalized Bernoulli, Euler and Genocchi numbers and polynomials.

Beih S. El-Desouky Rabab S. Gomaa Alia M. Magar

It is shown that the penetration of an oscillating electric field in a semi-infinite classical plasma obeys the standard exponential attenuation law $e^{-x/\lambda_{e}}$ (besides oscillations), where $x$ is the distance from the wall and $\lambda_{e}$ is the extinction length (penetration depth, attenuation length). The penetration depth is computed here explicitly; it is shown that it is of the order $\lambda_e \simeq [\mid\varepsilon \mid/(1-\varepsilon)]^{1/3}v_{th} / \omega$, where $\varepsilon$ is the dielectric function, $\omega$ is the frequency of the field and $v_{th}=\sqrt{T/m}$ is the thermal velocity ($T$ being the temperature and $m$ the particle (electron) mass). The result is obtained by including explicitly the contribution of the surface term.

M. Apostol

The quanta of electrical conductance is derived for a one-dimensional electron gas both by making use of the quasi-classical motion of a quantum fluid and by using arguments related to the uncertainty principle. The result is extended to a nanowire of finite cross-section area and to electrons in magnetic field, and the quantization of the electrical conductance is shown. An additional application is made to the two-dimensional electron gas.

M. Apostol

The effect of the electromagnetic radiation on the spontaneous charge emission from heavy atomic nuclei is estimated in a model which may be relevant for proton emission and alpha-particle decay in laser fields. Arguments are given that the electronic cloud in heavy atoms screens appreciably the electric field acting on the nucleus and the nucleus "sees" rather low fields. In these conditions, it is shown that the electromagnetic radiation brings second-order corrections in the electric field to the disintegration rate, with a slight anisotropy. These corrections give a small enhancement of the disintegration rate. The case of a static electric field is also discussed.

M. Apostol

It is suggested that the hadronization of the quark-gluon plasma is a first-order phase transition described by a critical curve in the temperature-(quark) density plane which terminates in a critical point. Such a critical curve is derived from the van der Waals equation and its parameters are estimated by using the theoretical approach given in M. Apostol, Roum. Reps. Phys. 59 249 (2007); Mod. Phys. Lett. B21 893 (2007). The main assumption is that quark-gluon plasma created by high-energy nucleus-nucleus collisions is a gas of ultrarelativistic quarks in equilibrium with gluons (vanishing chemical potential, indefinite number of quarks). This plasma expands, gets cool and dilute and hadronizes at a certain transition temperature and transition density. The transition density is very close to the saturation density of the nuclear matter and, it is suggested that both these points are very close to the critical point n~1fm^{-3} (quark density) and T~200MeV (temperature).

M. Apostol

Let $a$ and $b$ be relatively prime positive integers. In this paper the weighted sum $\sum_{n\in{\rm NR}(a,b)}\lambda^{n-1}n^m$ is given explicitly or in terms of the Apostol-Bernoulli numbers, where $m$ is a nonnegative integer, and ${\rm NR}(a,b)$ denotes the set of positive integers nonrepresentable in terms of $a$ and $b$.

Takao Komatsu Yuan Zhang

The coupling of photons with (ultra-) relativistic atomic nuclei is presented in two particular circumstances: very high electromagnetic fields and very short photon pulses. We consider a typical situation where the (bare) nuclei (fully stripped of electrons) are accelerated to energies ~1TeV per nucleon (according to the state of the art at LHC, for instance) and photon sources like petawatt lasers \simeq1eV -radiation (envisaged by ELI-NP project, for instance), or free-electron laser ~10keV -radiation, or synchrotron sources, etc. In these circumstances the nuclear scale energy can be attained, with very high field intensities. In particular, we analyse the nuclear transitions induced by the radiation, including both one- and two-photon processes, as well as the polarization-driven transitions which may lead to giant dipole resonances. The nuclear (electrical) polarization concept is introduced. It is shown that the perturbation theory for photo-nuclear reactions is applicable, although the field intensity is high, since the corresponding interaction energy is low and the interaction time (pulse duration) is short. It is also shown that the description of the giant nuclear dipole resonance requires the dynamics of the nuclear electrical polarization degrees of freedom.

M. Apostol M. Ganciu